Related papers: Bit Reversal through Direct Fourier Permutation Me…

Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and…

We have developed an algorithm for transferring radiation in three-dimensional space. The algorithm computes radiation source and sink terms using the Fast Fourier Transform (FFT) method, based on a formulation in which the integral of any…

Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schr\"odinger equation, which describes the evolution of the signal in the link, numerically.…

This article studies the inverse problem of recovering a vector field supported in $\mathbb{D}_R$, the disk of radius $R$ centered at the origin, through a set of generalized broken ray/V-line transforms, namely longitudinal and transverse…

This paper introduces the theory and hardware implementation of two new algorithms for computing a single component of the discrete Fourier transform. In terms of multiplicative complexity, both algorithms are more efficient, in general,…

Reversible contrast mapping (RCM) is a simple integer transform that applies to pairs of pixels. For some pairs of pixels, RCM is invertible, even if the least significant bits (LSBs) of the transformed pixels are lost. The data space…

Image reconstruction in Magnetic Resonance Imaging (MRI) is fundamentally a linear inverse problem, such that the image can be recovered via explicit pseudoinversion of the encoding matrix by solving $\textbf{data} = \textbf{Encode} \times…

This work introduces a general numerical technique to invert one dimensional analytic or tabulated nonlinear functions in assigned ranges of interest. The proposed approach is based on an optimal version of the k-vector range searching, an…

For a sample set of 1024 values, the FFT is 102.4 times faster than the discrete Fourier transform (DFT). The basis for this remarkable speed advantage is the `bit-reversal' scheme of the Cooley-Tukey algorithm. Eliminating the burden of…

Image inverse problems have numerous applications, including image processing, super-resolution, and computer vision, which are important areas in image science. These application models can be seen as a three-function composite…

In this paper we construct explicit sampling sets and present reconstruction algorithms for Fourier signals on finite vector spaces $G$, with $|G|=p^r$ for a suitable prime $p$. The two sets have sizes of order $O(pt^2r^2)$ and…

The Discrete Periodic Radon Transform (DPRT) has been extensively used in applications that involve image reconstructions from projections. This manuscript introduces a fast and scalable approach for computing the forward and inverse DPRT…

Sorting algorithms are the deciding factor for the performance of common operations such as removal of duplicates or database sort-merge joins. This work focuses on 32-bit integer keys, optionally paired with a 32-bit value. We present a…

Most of the well known algorithms for watermarking of digital images involve transformation of the image data to Fourier or singular vector space. In this paper, we introduce watermarking in Hilbert transform domain for digital media.…

Bit retrieval, the problem of determining a binary sequence from its cyclic autocorrelation, is a special case of the phase retrieval problem. Algorithms for phase retrieval are extensively used in several scientific disciplines, and yet,…

This paper introduces a factorization for the inverse of discrete Fourier integral operators that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a…

The deterministic recursive pivot-free algorithms for the computation of generalized Bruhat decomposition of the matrix in the field and for the computation of the inverse matrix are presented. This method has the same complexity as…

Recursive algorithms for computing the Frobenius norm of a real array are proposed, based on hypot, a hypotenuse function. Comparing their relative accuracy bounds with those of the BLAS routine DNRM2 it is shown that the proposed…

This paper presents ThielSort, a practical implementation of the Diverting Fast Radix (DFR) Algorithm. The theoretical improvements over classical radix sorts are outlined and implementation details are specified to demonstrate that the…

The standard dual-numbers construction works well for forward-mode automatic differentiation (AD) and is attractive due to its simplicity; recently, it also has been adapted to reverse-mode AD, but practical performance, especially on array…